parallel and perpendicular lines answer key

The coordinates of line 2 are: (2, -4), (11, -6) d = | x y + 4 | / \(\sqrt{2}\)} The symbol || is used to represent parallel lines. Step 2: (11x + 33)+(6x 6) = 180 Slope (m) = \(\frac{y2 y1}{x2 x1}\) We can observe that Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. 2x = 135 15 m = = So, slope of the given line is Question 2. y = -2x + b (1) (x1, y1), (x2, y2) The equation of the line along with y-intercept is: 180 = x + x A hand rail is put in alongside the steps of a brand new home as proven within the determine. Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals. So, ERROR ANALYSIS Hence, from the given figure, = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) We can conclude that So, then they are parallel to each other. 10) b = 9 \(\frac{8 (-3)}{7 (-2)}\) The slope of the equation that is perpendicular to the given equation is: \(\frac{1}{m}\) You are trying to cross a stream from point A. y = 2x + c In Exercises 11 and 12. prove the theorem. Hence, from the above, Answer: C(5, 0) We know that, We can conclude that Question 4. A(8, 0), B(3, 2); 1 to 4 b. c = 1 d = \(\sqrt{(x2 x1) + (y2 y1)}\) -x + 2y = 12 Thus the slope of any line parallel to the given line must be the same, \(m_{}=5\). -2 3 = c c = -4 The given points are: P (-5, -5), Q (3, 3) So, Question 5. m1 and m5 Justify your answers. Answer: Question 16. We can conclude that the consecutive interior angles of BCG are: FCA and BCA. Answer: According to the Vertical Angles Theorem, the vertical angles are congruent HOW DO YOU SEE IT? If the slope of AB and CD are the same value, then they are parallel. -9 = \(\frac{1}{3}\) (-1) + c are parallel, or are the same line. MAKING AN ARGUMENT So, Substitute A (3, 4) in the above equation to find the value of c c. If m1 is 60, will ABC still he a straight angle? 2 = 123 y = \(\frac{1}{2}\)x 7 Explain your reasoning. We can conclude that the distance from point A to the given line is: 6.26. The given figure is: The postulates and theorems in this book represent Euclidean geometry. We can observe that the given angles are the corresponding angles Answer: According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent Often you have to perform additional steps to determine the slope. m2 = \(\frac{1}{2}\), b2 = -1 We can conclude that the distance from point C to AB is: 12 cm. XY = \(\sqrt{(3 + 3) + (3 1)}\) -5 = \(\frac{1}{2}\) (4) + c Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\). a. Hence those two lines are called as parallel lines. -2 \(\frac{2}{3}\) = c Download Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav. Hence, p || q and q || r. Find m8. Hence, from the above, We can conclude that We can observe that there are a total of 5 lines. y = \(\frac{1}{2}\)x 2 To find the value of c, Given: a || b, 2 3 2: identify a parallel or perpendicular equation to a given graph or equation. A(2, 1), y = x + 4 c = 2 Compare the given equation with y = -2x + 1, e. = \(\frac{1}{3}\) Answer: Exercise \(\PageIndex{5}\) Equations in Point-Slope Form. From the given figure, 12y = 156 m2 = 1 To find the coordinates of P, add slope to AP and PB To find the value of c, P = (22.4, 1.8) y = \(\frac{1}{2}\)x 4, Question 22. Substitute (0, -2) in the above equation XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) plane(s) parallel to plane LMQ Line 1: (- 3, 1), (- 7, 2) \(\frac{1}{3}\)x + 3x = -2 + 2 c = -3 b. m1 + m4 = 180 // Linear pair of angles are supplementary We know that, Answer: Exploration 2 comes from Exploration 1 The converse of the given statement is: Now, So, (1) = Eq. \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\), \(\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.\), \(\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.\), \(\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.\), \(\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.\), \(\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.\), \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.\), \(\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.\). Answer: 15) through: (4, -1), parallel to y = - 3 4 x16) through: (4, 5), parallel to y = 1 4 x - 4 17) through: (-2, -5), parallel to y = x + 318) through: (4, -4), parallel to y = 3 19) through . We know that, Perpendicular to \(y3=0\) and passing through \((6, 12)\). c = -5 The following table shows the difference between parallel and perpendicular lines. We know that, We can conclude that the number of points of intersection of coincident lines is: 0 or 1. Hence, In Exercises 11-14, identify all pairs of angles of the given type. So, . = 320 feet Answer: Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. Is b c? When we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90, Work with a partner. c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. c = 12 So, 8x = 42 2 Consecutive Interior Angles Theorem (Thm. The given point is: P (4, 0) d = \(\sqrt{(x2 x1) + (y2 y1)}\) -2 = \(\frac{1}{3}\) (-2) + c We can conclude that the given pair of lines are parallel lines. A (-2, 2), and B (-3, -1) Answer: Question 26. The Converse of the Consecutive Interior angles Theorem: By using the parallel lines property, Therefore, the final answer is " neither "! m2 = -1 Label the ends of the crease as A and B. The painted line segments that brain the path of a crosswalk are usually perpendicular to the crosswalk. Supply: lamborghini-islero.com = \(\frac{-450}{150}\) The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) x = 5 and y = 13. For a square, We can conclude that the midpoint of the line segment joining the two houses is: MAKING AN ARGUMENT Substitute A (-6, 5) in the above equation to find the value of c P = (4, 4.5) Name two pairs of congruent angles when \(\overline{A D}\) and \(\overline{B C}\) are parallel? The adjacent angles are: 1 and 2; 2 and 3; 3 and 4; and 4 and 1 x = 4 So, The given equation is: Expert-Verified Answer The required slope for the lines is given below. From the given figure, We can observe that Example 5: Tell whether the line y = {4 \over 3}x + 2 y = 34x + 2 is parallel, perpendicular or neither to the line passing through \left ( {1,1} \right) (1,1) and \left ( {10,13} \right) (10,13). We can conclude that Answer: Answer: You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. We know that, THOUGHT-PROVOKING Parallel lines are those that never intersect and are always the same distance apart. Hence, The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. Where, Answer: Question 38. Think of each segment in the diagram as part of a line. 1 = 2 Given m3 = 68 and m8 = (2x + 4), what is the value of x? If the sum of the angles of the consecutive interior angles is 180, then the two lines that are cut by a transversal are parallel (b) perpendicular to the given line. m1 m2 = -1 w y and z x Each unit in the coordinate plane corresponds to 50 yards. A(1, 3), B(8, 4); 4 to 1 c = 5 Algebra 1 worksheet 36 parallel and perpendicular lines answer key. Identify all pairs of angles of the given type. Draw a third line that intersects both parallel lines. Compare the given points with The lines that are coplanar and any two lines that have a common point are called Intersecting lines Write an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2). Justify your conjecture. The given figure is: Compare the given points with In Exploration 2, Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. = \(\sqrt{(250 300) + (150 400)}\) These Parallel and Perpendicular Lines Worksheets will give the student a pair of equations for lines and ask them to determine if the lines are parallel, perpendicular, or intersecting. So, Answer: Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. Explain. Given 1 2, 3 4 x + 2y = 2 The Converse of the Alternate Exterior Angles Theorem: Step 1: Find the slope \(m\). a. Answer: x = \(\frac{-6}{2}\) In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also So, a. = 255 yards y = \(\frac{1}{2}\)x 6 2 = 140 (By using the Vertical angles theorem) The equation that is perpendicular to the given equation is: Hence, from the above, \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines The Converse of Corresponding Angles Theorem: We know that, We know that, Answer: Answer: d = | -2 + 6 |/ \(\sqrt{5}\) = 0 By using the Perpendicular transversal theorem, Question 1. plane(s) parallel to plane CDH The equation that is perpendicular to the given line equation is: = 180 76 We can observe that From the given figure, 3. plane(s) parallel to plane ADE Hence, from the above, Question 1. These guidelines, with the editor will assist you with the whole process. (5y 21) and 116 are the corresponding angles For parallel lines, we cant say anything y = -3x 2 (2) Answer: Question 48. We know that, Answer: Hence, from the given figure, From the given figure, The given point is: A (3, -4) Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. The coordinates of x are the same. PROBLEM-SOLVING a.) So, 9. We can conclude that the equation of the line that is parallel to the given line is: The converse of the Alternate Interior angles Theorem: 48 + y = 180 We can observe that the given angles are the corresponding angles Question 1. To find 4: We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The slopes are equal fot the parallel lines So, m1m2 = -1 Now, We can observe that a is perpendicular to both the lines b and c All the angles are right angles. So, c.) Parallel lines intersect each other at 90. The given equation is: We know that, Explain your reasoning. The given figure is: Slope of TQ = 3 Answer: c = -13 We know that, They both consist of straight lines. Answer: Question 18. The given figure is: (7x + 24) = 180 72 Hence, from the above, In Exercises 3 and 4. find the distance from point A to . We get y = -x + c Answer: Answer: The representation of the perpendicular lines in the coordinate plane is: In Exercises 21 24, find the distance from point A to the given line. Line 1: (- 9, 3), (- 5, 7) We know that, The equation of line p is: We can conclude that The given point is: (4, -5) A(- \(\frac{1}{4}\), 5), x + 2y = 14 These worksheets will produce 6 problems per page. The slopes of the parallel lines are the same The distance between the two parallel lines is: Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. y = 3x + c 4x + 2y = 180(2) Answer: Question 52. Explain your reasoning. We know that, The coordinates of the midpoint of the line segment joining the two houses = (150, 250) The given figure is: 10. Explain your reasoning. (C) Alternate Exterior Angles Converse (Thm 3.7) line(s) skew to The given equation is: Now, Answer: 2 = 180 47 Answer: So, how many right angles are formed by two perpendicular lines? The slope of first line (m1) = \(\frac{1}{2}\) This contradicts what was given,that angles 1 and 2 are congruent. Compare the given equation with c = -1 1 y = 132 = \(\frac{0 + 2}{-3 3}\) alternate interior We know that, Parallel lines XY = \(\sqrt{(6) + (2)}\) Hence, from the above figure, Then by the Transitive Property of Congruence (Theorem 2.2), _______ . Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. Begin your preparation right away and clear the exams with utmost confidence. So, Now, We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6. y = 3x 5 = 104 The representation of the given point in the coordinate plane is: Question 54. Answer: Question 30. So, Perpendicular to \(y=\frac{1}{3}x+2\) and passing through \((4, 3)\). y = -7x + c The Parallel and Perpendicular Lines Worksheets are randomly created and will never repeat so you have an endless supply of quality Parallel and Perpendicular Lines Worksheets to use in the classroom or at home. Label the point of intersection as Z. The product of the slopes of the perpendicular lines is equal to -1 From the given figure, Hence, from the above, \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). Which lines intersect ? From the given figure, Geometry chapter 3 parallel and perpendicular lines answer key. Substitute (4, 0) in the above equation Possible answer: 1 and 3 b. We know that, Now, line(s) skew to . In Exercises 11 and 12, describe and correct the error in the statement about the diagram. We know that, x + x = -12 + 6 Perpendicular lines are intersecting lines that always meet at an angle of 90. Answer: The given figure is: alternate interior d = \(\sqrt{(x2 x1) + (y2 y1)}\) We know that, Answer: Perpendicular to \(5x+y=1\) and passing through \((4, 0)\). The resultant diagram is: y = 3x 5 Solution to Q6: No. We know that, Question 9. THOUGHT-PROVOKING The parallel lines are the lines that do not have any intersection point All the angle measures are equal So, Answer: Explain your reasoning. then they are supplementary. It is given that m || n These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. Answer: y = \(\frac{1}{2}\)x + b (1) Hence, from the above figure, Solve each system of equations algebraically. 2. Hence, from the above, You and your family are visiting some attractions while on vacation. y = -3 (0) 2 2 = 0 + c MODELING WITH MATHEMATICS m2 = \(\frac{1}{2}\) The given figure is: Compare the given coordinates with (x1, y1), and (x2, y2) So, To find the coordinates of P, add slope to AP and PB d = \(\sqrt{(x2 x1) + (y2 y1)}\) Question 21. The given figure is: Proof: perpendicular lines. (x1, y1), (x2, y2) Answer: Question 38. x z and y z The given point is: A (-1, 5) -4 1 = b Hence, THOUGHT-PROVOKING c = 5 7 All perpendicular lines can be termed as intersecting lines, but all intersecting lines cannot be called perpendicular because they need to intersect at right angles. We can conclude that the claim of your classmate is correct. The equation of the perpendicular line that passes through (1, 5) is: So, We know that, = \(\frac{-4}{-2}\) Parallel Lines - Lines that move in their specific direction without ever intersecting or meeting each other at a point are known as the parallel lines. y = -2 (-1) + \(\frac{9}{2}\) We can conclude that the distance from point A to the given line is: 5.70, Question 5. For example, AB || CD means line AB is parallel to line CD. Answer: The equation of the line that is perpendicular to the given line equation is: The representation of the complete figure is: PROVING A THEOREM Answer: Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). The lines that do not intersect to each other and are coplanar are called Parallel lines 5 7 y = -2x + 2 y = 13 So, Hence, from the above, Find the Equation of a Parallel Line Passing Through a Given Equation and Point \(\frac{1}{2}\) (m2) = -1 Perpendicular lines meet at a right angle. What is the length of the field? So, y = \(\frac{8}{5}\) 1 m2 = -3 Slope of line 2 = \(\frac{4 + 1}{8 2}\) Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. (1) The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. XY = \(\sqrt{(3 + 3) + (3 1)}\) So, d. AB||CD // Converse of the Corresponding Angles Theorem. The given table is: y = x + 4 Now, PROOF Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Answer: Question 6. We can conclude that the parallel lines are: So, We can conclude that the value of x is: 14. The product of the slopes of perpendicular lines is equal to -1 Slope of TQ = \(\frac{-3}{-1}\) Question 15. Answer: 42 + 6 (2y 3) = 180 Explain your reasoning. Hence, from the above, y = 2x + c1 Answer: y = 27.4 So, then the slope of a perpendicular line is the opposite reciprocal: The mathematical notation \(m_{}\) reads \(m\) perpendicular. We can verify that two slopes produce perpendicular lines if their product is \(1\). Compare the given points with (x1, y1), (x2, y2) By using the Consecutive Interior Angles Theorem, Substitute A (8, 2) in the above equation If we draw the line perpendicular to the given horizontal line, the result is a vertical line. = \(\frac{5}{6}\) The slope is: 3 Compare the given equation with 5 = \(\frac{1}{3}\) + c We know that, XY = \(\sqrt{(3 + 3) + (3 1)}\) Now, The coordinates of line c are: (4, 2), and (3, -1) Hence, The given point is:A (6, -1) So, The given figure is: Now, In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary m || n is true only when 147 and (x + 14) are the corresponding angles by using the Converse of the Alternate Exterior Angles Theorem The given coordinates are: A (-2, 1), and B (4, 5) WHAT IF? The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. alternate exterior If we represent the bars in the coordinate plane, we can observe that the number of intersection points between any bar is: 0 By using the Perpendicular transversal theorem, It is given that a coordinate plane has been superimposed on a diagram of the football field where 1 unit is 20 feet. We know that, From the given figure, The given points are: It is given that a gazebo is being built near a nature trail. Hence, from the above, x = 133 In Exercises 15-18, classify the angle pair as corresponding. We know that, Which angle pair does not belong with the other three? Hence, from the above, (2, 7); 5 1 2 11 Hence, The angle at the intersection of the 2 lines = 90 0 = 90 Perpendicular Postulate: How do you know that n is parallel to m? Use the steps in the construction to explain how you know that\(\overline{C D}\) is the perpendicular bisector of \(\overline{A B}\). So, The completed table is: Question 1. We can conclude that \(\overline{K L}\), \(\overline{L M}\), and \(\overline{L S}\), d. Should you have named all the lines on the cube in parts (a)-(c) except \(\overline{N Q}\)? = \(\frac{15}{45}\) Let's try the best Geometry chapter 3 parallel and perpendicular lines answer key. By using the Corresponding Angles Theorem, Perpendicular Lines Homework 5: Linear Equations Slope VIDEO ANSWER: Gone to find out which line is parallel, so we have for 2 parallel lines right. From the given figure, From the given figure, The given equation is: Slope of line 1 = \(\frac{9 5}{-8 10}\) The given figure is: If two lines x and y are horizontal lines and they are cut by a vertical transversal z, then So, Hence, ABSTRACT REASONING \(m_{}=\frac{5}{8}\) and \(m_{}=\frac{8}{5}\), 7. Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org2001 September 22, 2001 9 Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given. We know that, Hence, from the above figure, Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal. She says one is higher than the other. The coordinates of line p are: Substitute A (-3, 7) in the above equation to find the value of c 1 = 2 = 150, Question 6. We can conclude that if you use the third statement before the second statement, you could still prove the theorem, Question 4. Note: Parallel lines are distinguished by a matching set of arrows on the lines that are parallel. m = -7 Hence, The given diagram is: Substitute A (-2, 3) in the above equation to find the value of c Consecutive Interior Angles Converse (Theorem 3.8) Question 15. The product of the slopes of perpendicular lines is equal to -1 y = -2x + c Question 12. y = 145 Hence, Question 37. Answer: We can conclude that m1 = 76 We can conclude that the third line does not need to be a transversal. In other words, if \(m=\frac{a}{b}\), then \(m_{}=\frac{b}{a}\). We can observe that x and 35 are the corresponding angles No, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal. = \(\frac{8 + 3}{7 + 2}\) y = -x + c

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